Related papers: Initial Semantics for higher-order typed syntax in…
We propose the first steps in the development of a tool to automate the translation of Redex models into a (hopefully) semantically equivalent model in Coq, and to provide tactics to help in the certification of fundamental properties of…
Dependently typed proof assistant rely crucially on definitional equality, which relates types and terms that are automatically identified in the underlying type theory. This paper extends type theory with definitional functor laws,…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
Inductive and coinductive types are commonly construed as ontological (Church-style) types, denoting canonical data-sets such as natural numbers, lists, and streams. For various purposes, notably the study of programs in the context of…
We describe a generic construction of non-wellfounded syntax involving variable binding and its monadic substitution operation. Our construction of the syntax and its substitution takes place in category theory, notably by using monoidal…
Higher-order beta-matching is the following decision problem: given two simply typed lambda-terms, can the first term be instantiated to be beta-equivalent to the second term? This problem was formulated by Huet in the 1970s and shown…
Semantic typing has become a powerful tool for program verification, applying the technique of logical relations as not only a proof method, but also a device for prescribing program behavior. In recent work, Yao et al. scaled semantic…
From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models…
We present an extension of System F with higher-order context-free session types. The mixture of functional types with session types has proven to be a challenge for type equivalence formalization: whereas functional type equivalence is…
We investigate the formal semantics of a simple imperative language that has both classical and quantum constructs. More specifically, we provide an operational semantics, a denotational semantics and two Hoare-style proof systems: an…
Semantic parsing has made significant progress, but most current semantic parsers are extremely slow (CKY-based) and rather primitive in representation. We introduce three new techniques to tackle these problems. First, we design the first…
We present the first mechanized, succinct, practical, complete, and proven-faithful semantics for a modern regular expression language with backtracking semantics. We ensure its faithfulness by proving it equivalent to a preexisting…
This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier $I$. $I$ forms a formula from two…
We present a framework for the formal meta-theory of lambda calculi in first-order syntax, with two sorts of names, one to represent both free and bound variables, and the other for constants, and by using Stoughton's multiple…
We present the design, implementation, and foundation of a verifier for higher-order functional programs with generics and recursive data types. Our system supports proving safety and termination using preconditions, postconditions and…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
With the rise of modern search and recommendation platforms, insufficient collaborative information of cold-start items exacerbates the Matthew effect of existing platform items, challenging platform diversity and becoming a longstanding…
In order to help students learn how to write mathematical proofs, we adapt the Coq proof assistant into an educational tool we call Waterproof. Like with other interactive theorem provers, students write out their proofs inside the software…
Recent work by (Richardson and Kuhn, 2017a,b; Richardson et al., 2018) looks at semantic parser induction and question answering in the domain of source code libraries and APIs. In this brief note, we formalize the representations being…
We develop the usage of certain type theories as specification languages for algebraic theories and inductive types. We observe that the expressive power of dependent type theories proves useful in the specification of more complicated…